Surveys in Differential Geometry, Volume 21 (2016)
Published: 7 July 2016
Publisher: International Press of Boston, Inc.
Hardcover
360 pages
9781571463227
This volume consists of articles by speakers at the Conference on Geometry and Topology held at Harvard University in 2014. Included are: Camillo De Lellis, on the size of the singular set of area-minimizing currents; Simon Donaldson, on Kahler?Einstein metrics and algebraic structures on limit spaces; Mark Gross, on theta functions and mirror symmetry; Nigel Hitchin, on Higgs bundles and diffeomorphism groups; Fernando Marques, on topology of the space of cycles and existence of minimal varieties; William Meeks, on constant mean curvature surfaces; Richard Thomas, on the proof of the KKV conjecture; Claire Voisin, on stable birational invariants and the Luroth problem; and Mu-Tao Wang, on energy, momentum, and center of mass in general relativity.
ISBN: 978-1-118-49345-8
352 pages
September 2016
This bookpresents material on both the analysis of the classical concepts of correlation and on the development of their robust versions, as well as discussing the related concepts of correlation matrices, partial correlation, canonical correlation, rank correlations, with the corresponding robust and non-robust estimation procedures. Every chapter contains a set of examples with simulated and real-life data.
Makes modern and robust correlation methods readily available and understandable to practitioners, specialists, and consultants working in various fields.
Focuses on implementation of methodology and application of robust correlation with R.
Introduces the main approaches in robust statistics, such as Huber’s minimax approach and Hampel’s approach based on influence functions.
Explores various robust estimates of the correlation coefficient including the minimax variance and bias estimates as well as the most B- and V-robust estimates.
Contains applications of robust correlation methods to exploratory data analysis, multivariate statistics, statistics of time series, and to real-life data.
Includes an accompanying website featuring computer code and datasets
Features exercises and examples throughout the text using both small and large data sets.
ISBN: 978-1-119-24352-6
544 pages
November 2016
Probability and Conditional Expectations bridges the gap between books on probability theory and statistics by providing the probabilistic concepts estimated and tested in analysis of variance, regression analysis, factor analysis, structural equation modeling, hierarchical linear models and analysis of qualitative data. The authors emphasize the theory of conditional expectations that is also fundamental to conditional independence and conditional distributions.
Probability and Conditional Expectations
Presents a rigorous and detailed mathematical treatment of probability theory focusing on concepts that are fundamental to understand what we are estimating in applied statistics.
Explores the basics of random variables along with extensive coverage of measurable functions and integration.
Extensively treats conditional expectations also with respect to a conditional probability measure and the concept of conditional effect functions, which are crucial in the analysis of causal effects.
Is illustrated throughout with simple examples, numerous exercises and detailed solutions.
Provides website links to further resources including videos of courses delivered by the authors as well as R code exercises to help illustrate the theory presented throughout the book.
ISBN: 978-1-119-28637-0
616 pages
January 2017
First issued in translation as a two-volume work in 1975, this classic book provides the first complete development of the theory of probability from a subjectivist viewpoint. It proceeds from a detailed discussion of the philosophical mathematical aspects to a detailed mathematical treatment of probability and statistics.
De Finetti’s theory of probability is one of the foundations of Bayesian theory. De Finetti stated that probability is nothing but a subjective analysis of the likelihood that something will happen and that that probability does not exist outside the mind. It is the rate at which a person is willing to bet on something happening. This view is directly opposed to the classicist/ frequentist view of the likelihood of a particular outcome of an event, which assumes that the same event could be identically repeated many times over, and the 'probability' of a particular outcome has to do with the fraction of the time that outcome results from the repeated trials.
MSJ Memoirs, Vol.33
2016, 154p, ISBN: 978-4-86497-034-1
The notion of stability for algebraic vector bundles on curves was originally introduced by Mumford, and moduli spaces of semi-stable vector bundles were studied intensively by Indian mathematicians. The notion of stability for algebraic sheaves was generalized to higher dimensional varieties. The study of moduli spaces of algebraic sheaves not only on curves but also on higher dimensional algebraic varieties has attracted much interest for decades and its importance has been increasing not only in algebraic geometry but also in related fields as differential geometry, mathematical physics.
Masaki Maruyama is one of the pioneers in the theory of algebraic vector bundles on higher dimensional algebraic varieties. This book is a posthumous publication of his manuscript. It starts with basic concepts such as stability of sheaves, Harder-Narasimhan filtration and generalities on boundedness of sheaves. It then presents fundamental theorems on semi-stable sheaves : restriction theorems of semi-stable sheaves, boundedness of semi-stable sheaves, tensor products of semi-stable sheaves. Finally, after constructing quote-schemes, it explains the construction of the moduli space of semi-stable sheaves. The theorems are stated in a general setting and the proofs are rigorous.
Hardcover | January 2017 ISBN: 9780691166148
312 pp. | 6 x 9 | 164 color illus. 9 line illus. 43 tables.
Have you ever played the addictive card game SET? Have you ever wondered about the connections between games and mathematics? If the answer to either question is “yes,” then The Joy of SET is the book for you! The Joy of SET takes readers on a fascinating journey into this seemingly simple card game and reveals its surprisingly deep and diverse mathematical dimensions. Absolutely no mathematical background is necessary to enjoy this book?all you need is a sense of curiosity and adventure!
Originally invented in 1974 by Marsha Falco and officially released in 1991, SET has gained a widespread, loyal following. SET’s eighty-one cards consist of one, two, or three symbols of different shapes (diamond, oval, squiggle), shadings (solid, striped, open), and colors (green, purple, red). In order to win, players must identify “sets” of three cards for which each characteristic is the same?or different?on all the cards. SET’s strategic and unique design opens connections to a plethora of mathematical disciplines, including geometry, modular arithmetic, combinatorics, probability, linear algebra, and computer simulations. The Joy of SET looks at these areas as well as avenues for further mathematical exploration. As the authors show, the relationship between SET and mathematics runs in both directions?playing this game has generated new mathematics, and the math has led to new questions about the game itself.
The first book devoted to the mathematics of one of today’s most popular card games, The Joy of SET will entertain and enlighten the game enthusiast in all of us.
Liz McMahon and Gary Gordon are professors of mathematics at Lafayette College. Hannah Gordon is a SET Grand Master and is studying health and nutrition. Rebecca Gordon teaches mathematics at Newark Academy. As a family, the coauthors have played SET together for more than twenty years.